预测基于密度矩阵的电子动力学的统计学习方法
Statistical learning method for predicting density-matrix based electron dynamics
摘要：
我们发展了一种统计方法，从电子密度矩阵的时间序列中学习分子的哈密顿矩阵。我们将之前的方法扩展到更大的分子系统，通过结合物理特性来降低维度，同时还利用正则化技术，如岭回归来解决多重共线性。通过学习的哈密顿量，我们可以求解时间相关的Hartree-Fock（TDHF）方程，以及时传播电子密度，并预测其在无场和有场情况下的动力学。我们观察到预测的动态和地面实况之间的密切的定量协议的两个字段关闭轨迹类似的训练数据，和字段的训练数据之外的轨迹。
英文摘要：
We develop a statistical method to learn a molecular Hamiltonian matrix from a time-series of electron density matrices. We extend our previous method to larger molecular systems by incorporating physical properties to reduce dimensionality, while also exploiting regularization techniques like ridge regression for addressing multicollinearity. With the learned Hamiltonian we can solve the Time-Dependent Hartree-Fock (TDHF) equation to propagate the electron density in time, and predict its dynamics for field-free and field-on scenarios. We observe close quantitative agreement between the predicted dynamics and ground truth for both field-off trajectories similar to the training data, and field-on trajectories outside of the training data.
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